Download Protostellar/PMS Mass Infall Luminosity Problem

Protostellar/PMS Mass Infall
and the
Luminosity Problem
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(Padoan, Haugbølle, & Nordlund 2014, arXiv:1407.1445)
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Paolo Padoan (ICREA - Un. Barcelona)
Troels Haugbølle (NBI - Un. Copenhagen)
Åke Nordlund (NBI - Un. Copenhagen)
Mass Infall
Mass infall onto the star+disk system, measured within a sphere of size Racc ≥ Rdisk
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NOT the ‘internal’ accretion from the disk to the star
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INFALL: simulated (PS and PMS) - not observed ACCRETION: observed (only PMS) - not simulated
Why do we study mass-infall?
It brings in the stellar mass and may be much
more complex than in spherical collapse models.
It may be strong during most of the planetformation epoch.
It may control the disk evolution and the internal
accretion, even during non-embedded phases.
It is easier to simulate than disk accretion, if
large scales are computed self-consistently.
The Plan
Simulate a large star-forming region, without
resolving disks, for over 3 Myr
Measure the infall rates on sink particles
Compare infall rates with observed accretion rate
of pre-main-sequence (PMS) stars
Assume infall rates are good proxy of accretion
rate also for young protostars
Predict luminosity of protostars and compare with
observed luminosity
Learn about origin of protostellar luminosity and
formation timescale of individual stars
The Simulation
Periodic box, random driving, isothermal E.O.S.
MHD, self-gravity, sink particles
αvir = 0.9; Ms = 10; Ma = 5 Lbox=4pc; n=800cm-3; T=10K; B0=7μG;
M=3000 M☉
2563 + 6 AMR levels: dx = 50 AU
Huge range of scales (1.6e4), but still designed to
avoid resolving protostellar disks.
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Sink formation:
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Sink formed above n=108 cm-3 (IMF complete to 0.03 M☉)
Accretion above n=100 cm-3 (dM/dt detected to 1014 M☉/yr)
Accretion sphere with Racc=8dx=400 AU (external accretion)
Closest allowed neighbor sink at Rexcl=16dx=800 AU
N-body code for sink interactions/binaries
Up to SFE=0.16 and 1300 sinks
Importance of the integration time:
To fully populate the Salpeter range of the IMF
To follow the infall/accretion during PMS (nonembedded class II and III sources)
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Before gravity: many tdyn to relax the turbulence After gravity: 3 tdyn = 3 tff = 3.2 Myr
Comparison with previous state-of-the-art simulations
Bate (2012-2014) - HD: 0.4 pc, 500 M☉ , tfinal = 0.09 Myr (183 stars)
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Krumholz et al. (2012) - HD:
0.46 pc, 1000 M☉ , tfinal = 0.02 Myr (158 stars)
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Myers et al. (2014) - MHD: 0.46 pc, 1000 M☉ , tfinal = 0.05 Myr (92 stars)
This work, Padoan et al. (2014) - MHD:
4.0 pc, 3100 M☉ , tfinal = 3.2 Myr (1300 stars)
10 times larger size
35-160 times longer integration time
7-14 times more stars
Very realistic density field and velocity power spectrum
with correct MHD slope down to the sonic scale.
X projection
y projection
1 pc
Evolution during 3.2 Myr, from 1 to 1,300 stars
Moving from density projection to 3D rendering
and gradually zooming in one can see that: !
The structure is truly filamentary in 3D.
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It remains filamentary down to the smallest
scales of mass infall.
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The small-scale filaments are integral part of the
large scale structure
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Very different from isolated spherical cores
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Example of structure around a newly-formed sink:
2e7
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1e7
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n (cm-3)
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M=.04 M☉
Age=.01 Myr
L=3 L☉
by Tim Sandstrom
NASA/Ames
The early infall is highly filamentary
accretion sphere
exclusion sphere
Sink volume extractions....
3000 AU
The late infall is Bondi-Hoyle like
SFR and IMF
SFRff = 0.035 for more that one
free-fall time of the mean density
Chabrier IMF complete to 0.03 M☉,
including a full Salpeter range
Very realistic star formation, ideal to study the long-term
evolution of the protostellar infall on a large sample
The ONC sample (Manara et al. 2012)
Simulation at 2.6 Myr: Infall rate ∼ observed accretion rate
The upper envelope is sensitive to age, but it should be higher than
that for the observed accretion rates, because some stars are still
embedded even after 0.5 Myr, and because of energy losses
between infall and accretion.
Observational sample
(Manara et al. 2014)
The Luminosity ‘Problem’
Protostars from the c2d project (Evans et al. 2009)
Bolometric Temperature (K)
The bolometric luminosities of protostars with detected sub-mm envelope
(filled circles) span three orders of magnitude (0.1 ≲ L☉ ≲ 100); without
detected envelopes, five orders of magnitudes (0.001 ≲ L☉ ≲ 100).
The Luminosity ‘Problem’
Given the realistic comparison of the infall rates with the observed
accretion rates of older PMS stars, we now estimate the accretion
luminosity of protostars assuming the infall rate is equal to the
accretion rate.
accretion luminosity
accretion+star+envelope
Protostars in Evans et al.
We can avoid the spectral index classification (which depends on
complex disk physics and geometry), and instead use the envelope
mass, as in the Herschel Orion Protostar Survey (HOPS, Manoj et al.
2013; Fisher et al. 2013; Stutz et al. 2013)
Herschel’s protostars in Orion
(Fisher et al. 2014)
However, this is still a rather poor indicator of age.
Loose relation between
M2500 and age (as between
spectral index and age)
Approximate correlation
of M2500 free-fall time
and mass infall rate
The Protostellar Luminosity Function
Only a qualitative comparison, because we are not tailoring the
simulation to any specific star-forming region.
Evans et al.’s full sample (class 0 to III),
1024 source from different regions (blue),
compared with our 631 sinks found at
t=2.6 Myr (black). Useful to compare the
underlying IMFs: We lack BDs and have
more massive stars than in the c2d sample.
Both LFs peak around 0.2 L☉
Evans et al.’s sub-sample with detected
envelopes (class 0 and I), 110 sources
(blue), compared with our 288 sinks with
M2500 > 0.001 M☉ at t=2.6 Myr (black).
Similar PLFs, apart from a few more
massive protostars in the simulation (11
sinks > 4 M☉)
Dunham et al. (2013) extended the c2D
sample from 112 to 230 protostars, but 100
of the new sources lacks sub-mm
detections, so their totoal luminosity is
underestimated by a factor of 2.6 on
average (could be up to 10). The low
luminosity tail of the PLF is very uncertain
Kryukova et al. (2012) 728 Sptizer sources,
from both low-mass and high-mass starforming regions (no sub-mm data, but
correction to extrapolate the bolometric
luminosity). Now that more massive
protostars are included, the match with
our PLF is much improved.
The PLF, like the underlying IMF, has region-to-region variations.
Do not take seriously the low-luminosity tail of the PLF. Good qualitative match between sink PLF and observed PLF.
The explanation of the luminosity scatter:
sinks # 25, 27, 80
1. Stars of either
different or equal
final mass can follow
very different tracks
of infall versus time.
sinks # 77, 79, 88
2. Individual stars,
(especially binaries,
but also single stars)
have tracks of infall
versus time with
huge oscillations.
Protostellar/PMS Binaries
The infall rate of the secondary grows by 2–3 orders
of magnitude at the approximate time of the periastro,
becoming comparable to the infall rate of the primary.
What is the characteristic timescale to form
a star, and how does it scale with final mass?
Age95% = 0.45 Myr (Mf/M☉)0.56
This applies to typical molecular clouds (Larson scaling relations).
The coefficient could be smaller or larger than 0.45 Myr in regions
that deviates significantly from Larson relations.
Conclusions
Mass infall controls the accretion rate of both
protostars and PMS stars. The luminosity problem is solved when realistic
protostellar initial and boundary conditions (and their
statistical distributions) are adopted (large-scale
simulation), under the reasonable assumption that the
mass infall controls the protostellar accretion rate. The observed large scatter of protostellar luminosities
is due both to star-to-star differences in the time
evolution of the infall rate and to large fluctuations of
the infall of individual stars (especially during binary or
multiple interactions).
Is external accretion really important, or am I
hiding a large fraction of non-accreting stars?
Most stars are accreting
Not much age dependence
Cumulative fraction including non-detections:
Can it be done for real star-forming regions?
External accretion can account for all (internally) accreting stars.